Preservation of Conditionally Nonblocking Switches Under Two-Stage Interconnection

The two-stage interconnection network is conceivably the most compact design for interconnecting small switches into a large switch. Switches so constructed typically can be controlled in the self-routing manner, because the route from an input to an output is unique. Different orderings of network input/output result in different versions of the two-stage interconnection network, two of which are known to preserve various classes of conditionally nonblocking switches. This paper adds Latin-square switches, rotators, reflectors, twisters, and untwisters to this set of classes with applications in load balancing, crosstalk-free optical switching, full connectivity among multiple users, etc. Knowledge of switch preservation under a certain style of multistage interconnection not only allows recursive construction of indefinitely large switches, but also provides insight, generality, and algorithmic flexibility in the construction